Abstract

The book is a monographic description of the present attempt to Newtonian and Lagrangian mechanics. But also, it could be found as a supplementary educational material useful for the graduate courses in mechanics taken by students majoring in mechanical engineering, physics or physical science. In the book you can find a brief introduction to concepts and principles of algebra of vectors; Kinematics of particles, mainly focused on non-Cartesian coordinates used in the description of the kinematics; Dynamics of particles; focused on Newton's laws of motion; motion of particles in one and in three dimensions; description of dynamics in inertial and non-inertial frames of reference; linear and angular momentums; work and energy principles; Kinematics and dynamics of spherical motion of rigid bodies; Euler’s angles; angular velocities and accelerations; conical surfaces of angular velocity vectors, steady precession, angular momentum of bodies that performs spherical motion, Euler’s equations of dynamics for bodies in spherical motion and their kinetic energy formulas; Kinematics and dynamics of general motion of rigid bodies; linear velocity and linear acceleration of points of the bodies; linear and angular momentum of rigid bodies; Newton-Euler’s dynamics equations; kinetic energy; Simplified theory of gyroscope; Mechanics express with the Lagrangian formalism; constraints and the constraint equations; main principles used in classifications of the constraints; generalized coordinates; virtual displacements and consequences of the virtual work principle; virtual velocities and the virtual power; generalized forces and the generalized equation of dynamics (d’Alembert’s principle); two types of Lagrange’s equations; some alternative principles of equilibrium.

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